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t I I G tx D v Gp re t h G Rh Is

g v fe G Iu fz r i ts id I

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f

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G Ih c D gu D ih D

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qp h d t ih Ip tr q gu Dh y id og h {p p é

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zj , j = 1, ..., J

g fh Gx I fh id pe p id

r I ie p Fe 4g I

ih q t id p g Ie qp h q D ih Dj id t ie p p id wg I i ye I I a d q h p pe Ix a

te id tr u i i I G

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Du {g iz Tr I te I Yh I g

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PC 54 52 R

q o Du p I D a q tp G

wd id e q h

x = (x1 , ..., xn )

y = (y1 , ..., yn )

I

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g

t t

fg ie g h p Ir p id ie

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id G d q re r ie e j t s e

f (x, y) = -yT x

²(x) = E (f (x, y))

n

14 54 54
éd

2 (x) minxRn (x) minxRn (x) minxR

PC 54 52 R PC 54 V2

nd

I

ih q D tr tp i I i i é ye

h(z ) =



2

z 0

exp{-t2 }dt x
j

h y

= ²(x) + ( ) (x), ( ) = > 0.5
j =1

0, j = 1, . . . , n.

xj = 1,

-R,

(2 - 1), x f (x, y)


ih ä P YF $( 87 éè

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Q PC 54 2

qp æ I " p d D p w D k c vg i

f

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j y


f (x,y) (

=

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1

(

0

2 2 - 1 =

(

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0

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-1

(2 - 1),

-1

(2 - 1)}2 (1 - ))

-1

,

h(z ) =

2

z 0

exp{-t2 }dt

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= ²(x) + 1( ) (x), 1( ) = = ( 2 exp{h

i g D h

PC 54 V2

m

1 = 2

(

0

PC 54 V2

m

h

PC 54 V2

m

u (

PC 54 V2

Iz id t ie g h I t tr q i qu ch h y

m

PC 54 V2

m

=

)

1 p(u)du = ~ 2
)-²(x) (x)

(

-

exp{-

PC 54 V2

PC 54 V2

=

)

p(y)dy

f (x, y) = u

)-²(x) (x)

exp{-

u2 ~ }du = ~ 2

u2 ~ 1 }du + = ~ 2 2
)-²(x) 2 (x)

(u= 2t) ~

1 exp{-t2 }dt + , 2

exp{-t2 }dt,

> 0.5.

i z

te q h

fz Is q h g h m g ih Ip qg e 4p id t ie p ye i p id I qp h id g G Fe G e Iz id t ie g h I t tr q i qu ch m
PC 54 52 R Q

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=

1 1-

PC 54 V2

m

=

1 1-

PC 54 V2

m

²(x) = (1 - )

PC 54 V2

=

m

(

=

=

(t= 2z )

(k =z 2 )

(u=²(x)+ (x)t,

)=²(x)+ (x))

2 (x) exp{-z }dz + z exp{-z 2 }dz = (1 - ) z z 2 2 ²(x) 2 (x) (1 - ) + exp{-k }dk = (1 - ) 2 (1 - ) k 2 2 2 = ²(x) + ( 2 (1 - ) exp{ })-1 (x) = 2 -1 = ( 2 exp{h (2 - 1)}2 (1 - ))-1 (x) + ²(x).

1 (1 - )

u (

u (

(u - ²(x))2 1 exp{- u }du = 2 2 (x) 2 (x) ) 1 t2 (²(x) + (x)t) exp{- }dt = 2 2 (1 - ) t

z

2

)

²(x) = -R.

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qy ih t D p t Dd ie g fh i p 5 h Gx Fe d I a I q ih Ij a I q ih Ij 54 h g
14 54
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v id d I I @ %l i

Iy iz ( v I I gz t g

ye id I I æe Fj t I Dp y I Dp y I I G

4 I p I G fz Is G e G e a I Tr Is

d q h i h I v q h d q ih Ij we i I

g h q t ~d } %z â q} Iu I G e ag t d i gu ih tp Iu tp d D D ae %} Yh a I p q t id i D rd Du d a R Is I q h g h Is p t d q i Iu q D t id æp e i te G e p ts d D id g qe t d p qe a h re Ir t Ir D {k I Dj qe p pe ix I tp % Dh cr d I Fj Iz id i F t qr ih j gh R åä ãâ ç ä ç âã D gh R åä ãâ æ ç âã D I G e Dp y (d R åä ãâ á ç âã D qg ih qp ih 4g te v s s D y d o I Dj qe p pe x Iz id t ie g h G re r d g
-R + 1( ) (x) min 2 (x) minxRn -R + ( ) (x) min
á
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PC 54 52 R PC 54 52 R

PC 54 V2 PC 54 V2

ih Dj qe p pe {x o I i D d qr i iz ie g ih qp ih j d d qr 4 Ir Fz 54 e Dj qe p pe {x te G "e q| ih "p e " i G d æ wd y d h I I G re r id Ip a e Dp y id Ip ng wd y id I qu ih I i I I I F gu h V t d tr q g ih qp t id og te F i tr q D y d T q ih qj D id g I I G pe Ix a i I I a Iz id G pe Gx Fe q 4 d t s fs ch m m Iz id I q h tr q q m m h z th æh v| ts or u id I G we i I g d fz as e Dp y id Ip g t ce l t q t id i D rd Du d f I t r id p wd y id I G qe p pe vx i I ie g fh I p id "g vu Is t ie p ye i t I g fd D h F
= -R + 1.64485 = 0.051091267, = -R + 1.28155 = 0.039585806. = 0.064325084, = 0.054579225.
PC 54 2 PC 54 52 SR

I Dj qe p pe fx u id I id I G pe Ix a i t I g d qu æh %l i g h g f ih I q æh q| ih "p d D k á ie g fh m I p id ig vu Is t ie p ye i t I g vd qe y @d @ h te q t id i D rd Du d " G ye D h Ds ih tp v te q ih r d Ir t I G e gu ih tp { i I o qu h q t id i D rd Du d o Iu I G e I Gp re r d n I I I p m G ye qx ih qp ih j ~e Yz qu h q t id i D rd Du d o Fu I i g ih qp ä p d I q h r qx ih qp ih wj i I Dj e D x td %s
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m = .001248838; 0.0 (0 0.001377956 V = 0.000967002 0.001048420

m

00168551; 0.001523505) 0.000967002 0.001048420 0.001204755 0.000810129 0.000810129 0.001165746 R = 0.001

f

0.95 0.90

0.95 0.90

x = (0; 0.386364; 0.613636) 2 (x ) = ( )2 = 0.001002945

F (x, ) = (1 - ) + J x
j

²(x) = -mT x

xT V x min

j =1

3

-1

0, j = 1, 2, 3.

xj = 1,

j =1 J

T (-yj x - )+ xR
3

-R,

xR3 , R

min .

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h tr td d
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f
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j

T -yj x - , z zj , j = 1, ..., J

(1 - ) + J

j

0,

j = 1, ..., J,

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R
3

I I q ih q tp p t id 5g Fr q G q id Ip q| p I Ds I q Dh h t i ih Is I æe d F e tp i q h D
zj R
3

Yh h t â ih qp

Gp e r q Ih i %g r h v ih vg Rh Is

o t D f G e p Fx e h tr q D

k I d ye I q

% I q d q Dp

I h g h z I e i é

p(y) =

p(y)

yj , j = 1, .., J

1 exp{- (V 2 (2 ) |V |

N (m, V )

xR3 ,zRJ ,R

V

-1

-1

min

u, u)}.

= AT A

ts G h "e Rh qx ih % j D h d I q

d q i q h G d
3

á

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z = Au



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e â4 E B HG E B 4 éB

id Dp y Rh i g I p p e I

q h a I tp

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q h a d g p fd ye

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d qu e ih h i p e g id vg i

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i ce Is vh t I vj

ie

ih h qu l id I t p q I ts r

g h Ip e q
14

Ip i g ih I Gp y id gh

Ip

z1 , z 2 , z

= 0.90 x = (0.002726; 0.385811; 0.611463) 0.90 = 0.041819 0.90 = 0.054753 = 0.95 x = (0; 0.386364; 0.613636) 0.95 = 0.049940 0.95 = 0.064857
PC 54 52 R PC 54 V2

t ~

qu gm q e æp

3

y u = y - m, z = Au z z1 , z2 , z

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z

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PC 54 52 R éè çæ å

Ip G rd id (W ie p id

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PC 54 2

x1 , ..., xn S

n

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c t i i g R

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i

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xi = c
i

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,

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new

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x

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